The President of Earth was a fictional character in The Adventures of Captain Proton holoprogram. In order to communicate with photonic lifeforms on the holodeck believing the simulation was real and only photonic lifeforms were real, The Doctor took on this role and convinced them to help Captain Proton to defeat Doctor Chaotica and his Army of Evil. (VOY: "Bride of Chaotica!")
In the novel Starfleet: Year One, United Earth is headed by a President. At the conclusion of the Earth-Romulan War and during the founding of the Federation in 2161, Lydia Littlejohn served as President of United Earth.
Though much of Starfleet: Year One has since been contradicted by Star Trek: Enterprise and subsequent novels, the Star Trek: Corps of Engineers novel The Future Begins featured a reference to President Littlejohn's leadership during the war while the character makes a brief appearance in Beneath the Raptor's Wing, the first novel in the Star Trek: Enterprise - The Romulan War duology. (United Earth is later said to be a parliamentary republic, with a President as head of state, and a Prime Minister - specifically, Nathan Samuels - as head of government.)